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Add magic square example
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‎source_code/magic_squares.ipynb‎

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{
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"cells": [
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "99dd3bd6-9c07-446e-adea-9101b0e1d033",
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"metadata": {},
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"outputs": [],
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"source": [
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"import itertools\n",
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"import math"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 2,
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"id": "28ce8741-bcb9-490d-86b0-c0a08da29743",
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"metadata": {},
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"outputs": [],
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"source": [
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"def create_square(elements):\n",
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" n = math.isqrt(len(elements))\n",
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" square = [[] for _ in range(n)]\n",
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" for i, element in enumerate(elements):\n",
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" square[i//n].append(element)\n",
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" return square"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 3,
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"id": "492cba61-0564-4ba2-ac31-d9d36ea1d8df",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[[1, 2, 3], [4, 5, 6], [7, 8, 9]]"
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]
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},
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"execution_count": 3,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"create_square(list(range(1, 10)))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 22,
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"id": "9c6de9a2-20dd-42b9-b9e6-dc29581d7bdf",
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"metadata": {},
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"outputs": [],
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"source": [
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"def is_magic_squuare(square):\n",
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" n = math.isqrt(len(square))\n",
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" diag_sum = sum(square[i + i*n] for i in range(n))\n",
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" for i in range(n):\n",
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" row_sum = sum(square[j + i*n] for j in range(n))\n",
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" if row_sum != diag_sum:\n",
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" return False\n",
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" for j in range(n):\n",
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" col_sum = sum(square[j + i*n] for i in range(n))\n",
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" if col_sum != diag_sum:\n",
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" return False\n",
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" return sum(square[i*n + (n - i - 1)] for i in range(n)) == diag_sum"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 5,
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"id": "4875036e-a4c4-4972-aed0-5752efccf6e6",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"False"
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]
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},
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"execution_count": 5,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"is_magic_squuare(list(range(1, 10)))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 6,
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"id": "9149cec0-7678-4001-afcb-b11190368737",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 6,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"is_magic_squuare([2, 9, 4, 7, 5, 3, 6, 1, 8])"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 7,
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"id": "ed9f69e1-3988-4d85-94c6-355a0c6de1e4",
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"metadata": {},
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"outputs": [],
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"source": [
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"def create_magic_square(n):\n",
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" symbols = list(range(1, n*n + 1))\n",
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" for elements in itertools.permutations(symbols):\n",
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" if is_magic_squuare(elements):\n",
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" return create_square(elements)\n",
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" return None"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 8,
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"id": "61864a59-91b8-4d57-9c29-e922a3e170db",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"[[2, 7, 6], [9, 5, 1], [4, 3, 8]]"
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]
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},
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"execution_count": 8,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"create_magic_square(3)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 16,
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"id": "b07909cd-7af9-4750-a996-55d954b482db",
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"metadata": {},
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"outputs": [],
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"source": [
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"def create_all_magic_square(n, is_verbose=False):\n",
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" symbols = list(range(1, n*n + 1))\n",
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" nr_squares = 0\n",
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" for elements in itertools.permutations(symbols):\n",
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" if is_magic_squuare(elements):\n",
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" yield create_square(elements)\n",
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" nr_squares += 1\n",
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" if is_verbose and nr_squares % 10_000_000 == 0:\n",
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" print(f'{nr_squares} tested')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 17,
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"id": "114e04e2-761a-4ee8-9b8d-8190cf57c98a",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"[[2, 7, 6], [9, 5, 1], [4, 3, 8]]\n",
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"[[2, 9, 4], [7, 5, 3], [6, 1, 8]]\n",
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"[[4, 3, 8], [9, 5, 1], [2, 7, 6]]\n",
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"[[4, 9, 2], [3, 5, 7], [8, 1, 6]]\n",
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"[[6, 1, 8], [7, 5, 3], [2, 9, 4]]\n",
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"[[6, 7, 2], [1, 5, 9], [8, 3, 4]]\n",
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"[[8, 1, 6], [3, 5, 7], [4, 9, 2]]\n",
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"[[8, 3, 4], [1, 5, 9], [6, 7, 2]]\n",
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"CPU times: user 437 ms, sys: 2.86 ms, total: 439 ms\n",
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"Wall time: 438 ms\n"
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]
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}
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],
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"source": [
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"%%time\n",
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"for square in create_all_magic_square(3):\n",
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" print(square)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "2f367b59-9545-4b11-a551-0d9c67372e1d",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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"10000000 tested\n",
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"20000000 tested\n",
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"30000000 tested\n"
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]
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},
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{
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"ename": "KeyboardInterrupt",
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"evalue": "",
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"output_type": "error",
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"traceback": [
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"\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
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"\u001b[0;31mKeyboardInterrupt\u001b[0m Traceback (most recent call last)",
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"File \u001b[0;32m<timed exec>:1\u001b[0m\n",
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"Cell \u001b[0;32mIn[16], line 5\u001b[0m, in \u001b[0;36mcreate_all_magic_square\u001b[0;34m(n, is_verbose)\u001b[0m\n\u001b[1;32m 3\u001b[0m nr_squares \u001b[38;5;241m=\u001b[39m \u001b[38;5;241m0\u001b[39m\n\u001b[1;32m 4\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m elements \u001b[38;5;129;01min\u001b[39;00m itertools\u001b[38;5;241m.\u001b[39mpermutations(symbols):\n\u001b[0;32m----> 5\u001b[0m \u001b[38;5;28;01mif\u001b[39;00m is_magic_squuare(elements):\n\u001b[1;32m 6\u001b[0m \u001b[38;5;28;01myield\u001b[39;00m create_square(elements)\n\u001b[1;32m 7\u001b[0m nr_squares \u001b[38;5;241m+\u001b[39m\u001b[38;5;241m=\u001b[39m \u001b[38;5;241m1\u001b[39m\n",
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"Cell \u001b[0;32mIn[4], line 3\u001b[0m, in \u001b[0;36mis_magic_squuare\u001b[0;34m(square)\u001b[0m\n\u001b[1;32m 1\u001b[0m \u001b[38;5;28;01mdef\u001b[39;00m \u001b[38;5;21mis_magic_squuare\u001b[39m(square):\n\u001b[1;32m 2\u001b[0m n \u001b[38;5;241m=\u001b[39m math\u001b[38;5;241m.\u001b[39misqrt(\u001b[38;5;28mlen\u001b[39m(square))\n\u001b[0;32m----> 3\u001b[0m diag_sum \u001b[38;5;241m=\u001b[39m \u001b[38;5;28msum\u001b[39m(square[i \u001b[38;5;241m+\u001b[39m i\u001b[38;5;241m*\u001b[39mn] \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n))\n\u001b[1;32m 4\u001b[0m \u001b[38;5;28;01mfor\u001b[39;00m i \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n):\n\u001b[1;32m 5\u001b[0m row_sum \u001b[38;5;241m=\u001b[39m \u001b[38;5;28msum\u001b[39m(square[j \u001b[38;5;241m+\u001b[39m i\u001b[38;5;241m*\u001b[39mn] \u001b[38;5;28;01mfor\u001b[39;00m j \u001b[38;5;129;01min\u001b[39;00m \u001b[38;5;28mrange\u001b[39m(n))\n",
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"\u001b[0;31mKeyboardInterrupt\u001b[0m: "
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]
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}
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],
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"source": [
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"%%time\n",
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"for square in create_all_magic_square(5, True):\n",
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" print(square)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 28,
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"id": "321565e9-d441-4b18-89d8-1aecca504140",
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"metadata": {},
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"outputs": [],
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"source": [
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"def create_magic_square(n):\n",
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" if n < 3:\n",
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" raise ValueError('array size needs to be at least 3')\n",
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" if n % 2 == 1:\n",
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" square = [0]*n**2\n",
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" i, j, value = 0, n//2, 1\n",
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" for start_value in range(1, n*n, n):\n",
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" for value in range(start_value, start_value + n - 1):\n",
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" square[i*n + j] = value\n",
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" i = (i - 1 + n) % n\n",
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" j = (j + 1) % n\n",
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" square[i*n + j] = value + 1\n",
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" i = (i + 1) % n\n",
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" return square\n",
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" else:\n",
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" raise NotImplementedError('algorithm not implement for even sizes')"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 32,
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"id": "9f162be1-1714-420c-815d-e4ca3e072926",
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"metadata": {},
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"outputs": [
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{
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"data": {
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"text/plain": [
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"True"
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]
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},
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"execution_count": 32,
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"metadata": {},
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"output_type": "execute_result"
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}
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],
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"source": [
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"is_magic_squuare(create_magic_square(7))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 18,
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"id": "d56a4ac6-0a6b-403a-8569-7471f9caa9d8",
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"metadata": {},
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"outputs": [],
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"source": [
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"def print_square(elements):\n",
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" n = math.isqrt(len(elements))\n",
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" for i in range(n):\n",
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" print(''.join(f'{value:5d}' for value in elements[i*n:i*n+n]))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": 33,
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"id": "a52776a3-c275-4fa9-bfdf-84217f40b9e8",
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"metadata": {},
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"outputs": [
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{
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"name": "stdout",
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"output_type": "stream",
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"text": [
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" 30 39 48 1 10 19 28\n",
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" 38 47 7 9 18 27 29\n",
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" 46 6 8 17 26 35 37\n",
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" 5 14 16 25 34 36 45\n",
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" 13 15 24 33 42 44 4\n",
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" 21 23 32 41 43 3 12\n",
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" 22 31 40 49 2 11 20\n"
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]
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}
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],
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"source": [
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"print_square(create_magic_square(7))"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "c66eb794-0068-4fb3-8097-304dddeeebf5",
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"metadata": {},
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"outputs": [],
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"source": []
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}
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],
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"metadata": {
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"kernelspec": {
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"display_name": "Python 3 (ipykernel)",
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"language": "python",
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"name": "python3"
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},
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"language_info": {
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"codemirror_mode": {
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"name": "ipython",
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"version": 3
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},
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"file_extension": ".py",
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"mimetype": "text/x-python",
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"name": "python",
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"nbconvert_exporter": "python",
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"pygments_lexer": "ipython3",
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"version": "3.11.2"
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}
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},
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"nbformat": 4,
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"nbformat_minor": 5
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}

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